You can insert manual "word split markers" (not sure if this is the correct latex term), e.g. \- after every single digit, then latex will be able to split the number where ever needed. Maybe it is possible to make a latex macro to do this, but I do not know enough latex to do this, so I will use the commandline instead.
Example
\documentclass[a4paper,10pt]{scrartcl}
\usepackage{xltxtra}
\begin{document}
$\pi \approx \frac{22}{7} = NUMBER\ldots$
\end{document}
Running the command
echo "scale=200; 22/7" | bc -l | tr -d '\012\\' | sed 's/\(.\)/\1\\-/g' | xclip -i
and then pasting in the clipboard content replacing NUMBER above gives the following output:
π ≈ 22/7 = 3.1428571428571428571428571428571428571428571428571428571428571-
428571428571428571428571428571428571428571428571428571428571428571428571428-
5714285714285714285714285714285714285714285714285714285714285714...
The command to add \- after every single digit is sed 's/\(.\)/\1\\-/g'.
\-with\ifmmode\allowbreak\else\hspace{0pt plus 1pt}\fiBUT that makes the first line of the sequence overlap by one character. I haven't thought much how to fix that. – Alan Munn Mar 17 '11 at 00:39